Abstract
The notion of mod-φ convergence has been studied in the articles [JKN11, DKN15, KN10, KN12, BKN14], in connection with problems from number theory, random matrix theory and probability theory. The main idea was to look for a natural renormalisation of the characteristic functions of random variables which do not converge in law (instead of a renormalisation of the random variables themselves). After this renormalisation, the sequence of characteristic functions converges to some non-trivial limiting function. Here is the definition of mod-φ convergence that we will use throughout this chapter (see Section 1.5 for a discussion on the different parts of this definition).
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Féray, V., Méliot, PL., Nikeghbali, A. (2016). Introduction. In: Mod-ϕ Convergence. SpringerBriefs in Probability and Mathematical Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-46822-8_1
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